Physics formula
How projectile motion is calculated
Projectile motion combines constant horizontal velocity with vertical acceleration caused by gravity. The launch velocity is resolved into horizontal and vertical components before range, height, and flight time are calculated.
The standard model assumes negligible air resistance and equal launch and landing heights. Real-world results can differ when drag, wind, or elevation changes are significant.
Worked example
Projectile launched at 20 m/s and 45 degrees
Consider a projectile launched at 20 m/s at an angle of 45° using gravitational acceleration g = 9.81 m/s².
Range = v² sin(2θ) ÷ g
Range = 20² × sin(90°) ÷ 9.81 ≈ 40.8 m
The ideal horizontal range is approximately 40.8 metres. The calculated flight time is about 2.88 seconds, and the maximum height is about 10.2 metres.
Model limitations
Assumptions and limitations
The standard equations assume constant gravity, negligible air resistance, no wind, and equal launch and landing elevations.
Results may be inaccurate for aerodynamic objects, long-range trajectories, strong wind, changing elevation, spin effects, or launch conditions where drag cannot be ignored.
Related motion calculators
Study vertical motion independently with the Free Fall Calculator.
Calculate changes in velocity with the Acceleration Calculator.
Common questions
Projectile motion calculator FAQs
What is projectile motion?
Projectile motion describes an object moving horizontally while gravity accelerates it vertically.
What launch angle gives the greatest range?
In the ideal model with equal launch and landing heights and no air resistance, a 45-degree launch angle gives the greatest range.
Does the projectile motion calculator include air resistance?
No. It uses the standard ideal projectile model and assumes negligible drag and wind.
Why are horizontal and vertical velocity calculated separately?
Horizontal velocity remains constant in the ideal model, while vertical velocity changes because of gravitational acceleration.